The Activity Of A Radioactive Nucleus

Transcription

1 The Activity Of A Radioactive Nucleus Activity = the number of nuclei decaying per second Symbol A Unit Becquerel (Bq) 1 Bq = 1 disintegration per second 1

2 The Law Of Radioactive Decay Activity depends on??? Random process Therefore impossible to Huge numbers (10 23??) Therefore Activity α N N = number of radioactive nuclei Rate of decay 2

3 The Law Of Radioactive Decay A α N 1,000,000 radioactive nuclei Activity = 80 Bq 500,000 radioactive nuclee Activity = 40 Bq 250,000 radioactive nuclei Activity = 20 nuclei Etc. 3

4 The Law Of Radioactive Decay A α N Rate of decay = λ N A = λ N λ = decay constant Each radioactive isotope has its own λ 4

5 a knock on effect of the Law of Radioactive Decay or The time taken for half the undecayed nuclei to decay The time taken for the activity to halve 5

6 Half Life Values from fractions of a second to thousands of years Lead 214 = 27 min Uranium 238 = 4.5 x 10 9 y Carbon 14 = 5,800 y Radon 220 = 54.5 s 6

7 Example T 1/2 = 3 hours Say 1,000,000 radioactive nuclei now!! 3 1,000, , , ,000 3 T 1//2 is independent of N 0 (due to Law of Radioactive Decay) 7

8 Graph Activity vs. Time A X ½X time time T 1/2 8

9 Graph Activity vs. Time 9

10 P4 A radioactive isotope has a half life of 5 years. What fraction of the original sample will remain after 20 years? What fraction of the original sample will have decayed in 20 years? 20 years = 4 half lives /16th remains undecayed 15/16ths has decayed 10

11 P4 A radioactive isotope has a half life of 5 years. What fraction of the original sample will remain after 20 years? What fraction of the original sample will have decayed in 20 years? Note: After n half lives 1/2 n of the original sample remains undecayed. 1/2 4 undecayed 11

12 P6 The activity of a sample of a radioactive isotope decreases to 1/32 of its original value after 250 years. What is its half life? 1/32 = 1/2 5 5 half lives T 1/2 = 50 years 12

13 P7 The isotope Sr 90 decays by beta emission and has a decay constant of 8 x s 1. Calculate the number of atoms present in a sample of that isotope which emits 2.4 x 10 4 beta particles per second. Rate of decay = λ Ν 2.4 x 10 4 = (8 x ) N N = 3 x nuclei 13

14 P9 The half life of U 235, which is an alpha emitter, is 8 x 10 8 years. Find the number of alphaparticles emitted per second from a sample containing 2.6 x atoms. Number of particles emitted per second Rate T 1/2 of = decay = λn λ = Rate of decay = λ Ν Rate of decay = λ (2.6 x ) Rate of decay = (0.693 T 1/2 ) (2.6 x ) = 7.1 x 10 7 Bq 14

15 Geiger Müller Tube (GM tube) Solid State Detector 15

16 GM Tube 1908 Hans Geiger 1928 Geiger & Müller..Improved version 16

17 GM Tube Parts Tube (Cathode) Thin wire (Anode) Argon gas at low pressure Thin mica window 450 V Amplifier & Counter 17

18 GM Tube How It Works Radiation in through thin window Radiation ionises the argon gas Electrons accelerated by p.d. to thin wire (and ions accelerated to tube) Avalanche Effect (Electrons.. collisions.. huge number of electrons & ions) Electrons reach wire = Pulse of current Current pulse is counted on Scalar 18

19 GM Tube Counters Scalar Gives total number of counts Ratemeter Gives number of counts per second 19

20 Solid State Detector P DL N To amplifier & counter Radiation TW PN junction Suitable material (e.g. GaAS) Junction near the surface Reverse biased Thin window 20

21 Solid State Detector DL How It Works P N To amplifier & counter Reverse biased DL No conduction Radiation into DL Producing electron hole pairs (e, h + ) Pd moves these (e, h + ) pairs = current pulse that is amplified and counted (Scalar) Radiation TW 21

22 Detectors: Effectiveness In Detecting α, β, γ α β γ GM tube Good if window is thin Very good Poor (causes little ionisation) Solid State Detector Very good Good if suitable material used for junction Good if suitable material used for junction 22

23 Many isotopes are made radioactive by bombarding their nuclei with neutrons Done in Nuclear Reactors 23

24 Medical Imaging Medical Therapy Food Irradiation As Radioactive Tracers Carbon Dating Industry thickness of objects, fullness of containers, find leaks, etc. Smoke Detectors etc. 24

25 Cancer cells are more easily damaged than healthy cells High doses directed at cancer cells Co 60 X rays also used 25

26 Bacterial killed by radiation Sterilise medical equipment Sterilise food 26

27 Short half life Pipes for leaks Medical Agriculture Technicium 99 (β) (Injected to check the functioning of brain, kidneys, bones) Xenon 133 (β) a gas (Inhaled to check the functioning of the lungs) 27

28 Uptake of fertiliser by a plant Phosphorous 32 Radioactive fertiliser injected into soil Leaves checked for radioactivity 28

29 Am 241 (α) Ionises the air Current flows Smoke clings to ions Current is reduced Triggers alarm 29

30 C 14 T 1/2 = 5730 y All living things (plants & animals) Have a fixed amount of C 14 On dying C 14 levels decrease Things dated by measuring the C 14 to C 12 ratio 30

31 Turin Shroud shown to be 13 th century 31

32 Sheet metal, paper, plastic Too thick / thin Less / more radiation Activates pressure rollers to 32

33 Medical Imaging Medical Therapy Food Irradiation As Radioactive Tracers Carbon Dating Industry thickness of objects, fullness of containers, find leaks, etc. Smoke Detectors etc. 33

34 The 12 C 6 atom has 12 unified atomic mass units (u) Therefore 1 u is th the mass of the 12 C 6 atom 34

35 A mole of 12 C 6 has a mass of 12 g A mole of C 12 contains 6.02 x atoms. A mole of any substance contains 6.02 x particles. 35

36 235 U 92 1 mole = 235 g 235 g contains 6.02 x atoms (or nuclei) 60 Co 29 1 mole = 60 g 60 g contains 6.02 x atoms (or nuclei) 36

37 P10 How many atoms are there in 10 kg of 207 Pb 82? 1 mole = 207 g kg has 6.02 x atoms 1 kg has 6.02 x atoms 10 kg has (6.02 x ) x 10 atoms = 2.9 x atoms 37

38 P11 The decay constant of U 235 which is an alphaemitter is 2.75 x s 1. Find the number of alpha particles emitted per second from a 1 kg sample of this substance. Number of α s per second = Rate of decay = λ N = (2.75 x ) (6.02 x x 1000/235) = 7.0 x